Question: $g(t) = -5t+3-5(h(t))$ $h(n) = n^{2}+3n$ $ h(g(-1)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = (-5)(-1)+3-5(h(-1))$ To solve for the value of $g$ , we need to solve for the value of $h(-1)$ $h(-1) = (-1)^{2}+(3)(-1)$ $h(-1) = -2$ That means $g(-1) = (-5)(-1)+3+(-5)(-2)$ $g(-1) = 18$ Now we know that $g(-1) = 18$ . Let's solve for $h(g(-1))$ , which is $h(18)$ $h(18) = 18^{2}+(3)(18)$ $h(18) = 378$